Fiber_Optics_Physics_Technology

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Figure 9.25: The backscattered wave (the Stokes wave) has a deep and irregular temporal modulation, a result of the origin of the Stokes wave in spontaneous scattering processes.

Figure 9.26: The Fourier spectrum pertaining to the data shown in Fig. 9.25. The modulation of the Stokes wave extends up to tens of megahertz. This bandwidth is related to the damping rate of the acoustic wave in the nanosecond regime.

presence of optical feedback by reflection at the fiber ends, a resonator is formed; its round trip frequency (the inverse of its round trip time) constitutes a preferred frequency. If the reflections are strong enough, the modulation turns from irregular to periodic with nearly this frequency [39].

Without feedback, this modulation contains frequencies up to nearly 100 MHz. This limit is related to the damping rate of phonons, which is a few nanoseconds and which also sets the spectral width of the Stokes wave. Therefore, the Brillouin line width (SBS line width) is about νB ≈ 10 MHz, corresponding to a relative width of 10−3.

There is an important conclusion with regard to some fiber applications here. It is often the case that in laser-based materials processing the laser power must

be delivered from a bulky laser head to various positions on the workpiece. Fiber would provide perfect flexibility here, but SBS poses a severe limitation, and renders the idea to transmit sheer power useless unless extra measures are taken.

One such measure can be to avoid near-monochromatic pump light. For broadband pump light (band width νp), the e ective Brillouin gain is reduced according to

νB

g˜B = gB νB + νp .

For short pulses of light, the threshold is then higher because the pulse is spectrally wider than the SBS line width. The consequence is that for short, i.e., broadband, pulses, the threshold becomes much higher than the SRS threshold when the pulses have picosecond width. In that case SBS loses its importance.

We should also point out that the Brillouin gain mechanism, most often a nuisance, can in some cases actually be desirable. It can be exploited to build a Brillouin laser which can provide laser oscillation on a frequency o set from the pump by one Brillouin shift. Since the latter is within the reach of direct electronic detection, such lasers have uses in certain heterodyning applications. Moreover, there are Brillouin e ect-based sensors which can, e.g., exploit the temperature dependence of the Brillouin frequency to assess temperature. In combination with (long) pulses and an evaluation of the temporal structure, one can even have a position-resolved measurement. Fiber-optic sensors are treated in Chap. 12.

9.7.2Stimulated Raman Scattering

We have seen that the frequency shift in the case of Brillouin scattering is about 10 GHz. Stimulated Raman scattering (SRS) typically causes a frequency shift of 10 THz or a relative shift of 10−1. Therefore, for SRS, we cannot use the approximation ωp/ωs ≈ 1 as we did for SBS.

Other than that we can describe the power of the SRS Stokes wave as a function of position in the fiber in analogy to the above. We obtain

The gain factor g is about gR = 0.1 pm/W. The corresponding equation for the pump wave is

Again we convince ourselves that in the lossless case (αs = αp = 0), the photon number is preserved:

Figure 9.30: A Raman laser using a cascade of several Raman orders for the generation of light with longer wavelength. Several selective reflectors (fiberBragg gratings) form nested cavities which support the pump wave, the targeted Stokes order, and all intermediate orders. The numbers shown in the example refer to the case described in [58] where fifth-order Raman scattering transfers power from a pump wave at 1,117 nm to a new wavelength of 1,480 nm. After [58].

1.12 or 1.40 μm, respectively – certainly not ideally suited wavelengths for the purposes of fiber optics.

If the Stokes wave has su cient intensity, it can itself act as pump wave for another scattering process; this way a second scattered wave can be generated, and even higher orders may be generated, too. Figure 9.29 shows a case in which no less than five Stokes orders appear [36]. In devices called Raman cascade lasers as shown in Fig. 9.30 this can be utilized in an arrangement of nested cavities for several Stokes orders to transfer power across larger frequency di erences (see, e.g., [41]).

When Raman gain is used to provide gain for a signal transmitted through the fiber, it should be clear that su cient pump power must be available and that the pump frequency must ideally be 13 THz above the signal frequency. Fortunately, the Raman process is not sharply resonant but fairly broadband so that there is some tolerance in the signal frequencies suitable for a given pump. Active fibers like Er-doped fibers described above (Sect. 8.8.1) have a much narrower gain band, fixed once and for all by properties of the Er ion. They are therefore not as universally applicable. As increasingly massive wavelength division multiplex transmission is employed to make use of an ever-increasing bandwidth (see Sect. 11.1.5), the Er gain band begins to be a limitation for state-of-the-art systems. Raman amplifiers therefore attract more attention again recently.

Chapter 10

A Survey of Nonlinear

Processes

10.1Normal Dispersion

10.1.1Spectral Broadening

Self-phase modulation (SPM) broadens the frequency spectrum. This e ect is not pronounced as long as the peak nonlinear phase shift remains below π or so. At a few π, however, the spectrum begins to develop strong undulations as shown in Fig. 10.1.

Figure 10.1: Calculated spectral broadening by SPM; the maximum nonlinear phase shift is given as a parameter. From [146] with kind permission.

The figure is based on numerical calculations based on the nonlinear Schr¨odinger equation. This prediction is borne out well by experiment, as shown in Fig. 10.2. Intense light pulses in su ciently long fiber easily achieve φnl π. Then the spectrum takes a nearly rectangular shape (Fig. 10.3), mostly an e ect of the linear chirp across the central part of the pulse.

c Springer-Verlag Berlin Heidelberg 2009

generation of shorter pulses. In other words, strong self-phase modulation is a step toward pulse compression.

10.1.2Pulse Compression

Let us assume that a light pulse has assumed a broad spectrum by self-phase modulation. Then, there will be a strong chirp in its temporal evolution.

Now, if all this happens in the presence of normal dispersion, the di erent spectral components of the pulse will be stretched out temporally. Then, the pulse will take on a nearly rectangular temporal profile with a very nearly linear chirp when the components responsible for the flat central part of the spectrum are rearranged in time.

By using a di raction grating, one can generate an opposite (anomalous) dispersion which can recompress the distorted pulse to the shortest duration compatible with its spectral width. A pair of gratings (see Fig. 10.4) is more convenient to handle. A combination of a fiber and a grating pair as sketched in Fig. 10.5 is available commercially as a pulse compressor. It works in the wavelength regime where the fiber is normally dispersive (which is useful for light from dye lasers or Nd:YAG lasers), and it can considerably reduce the pulse duration, as shown in Figs. 10.6 and 10.7.

θ

blue

red

blue

red

Figure 10.4: Schematic representation of dispersion from a pair of di raction gratings. Shorter wave light (labelled as ‘blue’) takes a shorter path than longer wavelength light (‘red ’).

10.1.3Chirped Amplification

There are now laser systems capable of generating peak powers of more than 1 PW. They rely on an oscillator–amplifier concept: Pulses generated by an oscillator are amplified and brought well into the terawatt regime and above. Such light sources are important tools for basic physics research.

The technical di culty is that optical components of the amplifier must withstand the enormous intensities and thus are subject to a damage hazard.

Figure 10.5: Pulse compression with fiber and grating pair. The fiber generates strongly chirped pulses due to self-phase modulation. With a grating arrangement of judiciously chosen dispersion the chirp is compensated, and the pulse duration is reduced in the process. The figure shows a setup with double pass through a grating pair and output coupling from a beam splitter (partially reflecting mirror).

Autocorrelator signal

Time (ps)

Figure 10.6: Experimental result with fiber-grating compressor: Here pulses of initial width 33 ps were compressed down to 410 fs. From [76] with kind permission.

This can be avoided by the concept of “chirped pulse amplification” or CPA [126], which has its origin in radar technology and is a method to avoid high peak powers acting on components. One inserts a dispersive element – either a fiber or a grating – after the oscillator to produce a strong dispersive broadening of the pulse, with the accompanying reduction in peak power. The spectral components of the pulse then do not occur at the same time but sequentially. This predistorted pulse is fed to the amplifier where the highest intensity peaks are now reduced by the broadening factor. This can amount to several orders of magnitude, and the damage risk is drastically reduced. After amplification, all Fourier components are shifted together again by sending the pulses through another dispersive element which has the same absolute value of dispersion, but